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Mathematics 2017, 5(1), 12; doi:10.3390/math5010012

Fractional Fokker-Planck Equation

1
Mathematics Department, German University in Cairo, New Cairo City 11835, Egypt
2
University of Ulm, D-89069 Ulm, Germany
3
University of Utah, Salt Lake City, UT 84112, USA
In memoriam Th.F. Nonnenmacher.
*
Author to whom correspondence should be addressed.
Academic Editor: Rui A. C. Ferreira
Received: 27 October 2016 / Revised: 13 January 2017 / Accepted: 3 February 2017 / Published: 11 February 2017
(This article belongs to the Special Issue Fractional Differential and Difference Equations)
View Full-Text   |   Download PDF [6132 KB, uploaded 21 February 2017]   |  

Abstract

We shall discuss the numerical solution of the Cauchy problem for the fully fractional Fokker-Planck (fFP) equation in connection with Sinc convolution methods. The numerical approximation is based on Caputo and Riesz-Feller fractional derivatives. The use of the transfer function in Laplace and Fourier spaces in connection with Sinc convolutions allow to find exponentially converging computing schemes. Examples using different initial conditions demonstrate the effective computations with a small number of grid points on an infinite spatial domain. View Full-Text
Keywords: sinc methods; approximation; computation; integral equations; Riesz-Feller derivative; Caputo derivative; fractional Fokker Planck equation sinc methods; approximation; computation; integral equations; Riesz-Feller derivative; Caputo derivative; fractional Fokker Planck equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Baumann, G.; Stenger, F. Fractional Fokker-Planck Equation. Mathematics 2017, 5, 12.

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